1. Field of the Invention
This invention relates, generally, to cooling layers for printed circuit boards (“PCBs”). More particularly, it relates to dendritic cooling layers for multilayer PCBs and a method of generating a dendritic high conductivity path suitable for PCBs.
2. Description of the Prior Art
Several passive and active cooling systems are known in the art. However, conventional cooling systems are not effective when PCBs are operating at higher processing speeds.
Bejan volume (Bejan, A., 1997, Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume, International Journal of Heat and Mass Transfer, Vol. 40, No. 4, pp. 799-816) presented the Constructal Theory by solving an optimization problem for the cooling of a heat-generating surface. The proposed problem was “how to collect and channel to one point the heat generated volumetrically in a low conductivity volume of given size”.
Based on Constructal Theory, several authors have solved similar problems for different geometries and assembly levels. These solutions are not restricted to heat conduction; they cover a wide variety of optimization problems where the flow resistance of a given entity can be minimized. The flowing entity can be energy in the form of heat (Wei, S., Chen, L., Sun, F., 2009, The Area-point Constructal Optimization for Discrete Variable Cross-section Conducting Path, Applied Energy, Vol. 86, pp. 1111-1118), fluid (Wechsatol, W., Ordonez, J. C., Kosaraju, S., 2006, Constructal Dendritic Geometry and the Existence of Asymmetry Bifurcation, Journal of Applied Physics, Vol. 100, pp. 113514; also Rocha, L. A. O., Lorente, S., Bejan, A., 2009, Treeshaped Vascular Wall Designs for Localized Intense Cooling, International Journal of Heat and Mass Transfer, Vol. 52, pp. 4535-4544), aggregates of organisms (Miguel, A. F., Bejan, A., 2009, The Principle that Generates Dissimilar Patterns Inside Aggregates of Organisms, Physica A, Vol. 388, pp. 727-731) or even people (Reis, A. H., 2008, Constructal View of the Scaling Laws of Street Networks—The Dynamics Behind Geometry, Physica A, Vol. 387, pp. 617-622).
According to Ledezma et al. (Ledezma, G. A., Bejan, A., Errera, M. R., 1997, Constructal Tree Networks for Heat Transfer, Journal of Applied Physics, Vol. 82, No. 1, pp. 89-100), the major difficulty with the optimization of higher order assembles is the increasing number of degrees of freedom to be optimized. As such, a solution is needed to resolve this difficulty.
There are similar algorithms in the literature as well. In the work of Errera et al. (Errera, M. R., Bejan, A., 1998, Deterministic Tree Networks for River Drainage Basin, Fractals, Vol. 6, No. 3, pp. 245-261), dendritic patterns formed by low-resistance channels in a river drainage basin were reproduced by a porous media model where the drainage channels were predicted using Constructal Theory. In their solution, Darcy's Law was used to formulate the problem and the computational domain was divided in small blocks, which were initialized with a base permeability k0. The first step of the methodology was to determine the pressure field inside the computational domain and use it to estimate the pressure gradients. The process started with the replacement of the block that has the outlet port as one of its four sides. In a second step, the pressure gradient of all neighbors of this first block was calculated. If one or more of these gradients was higher than a predefined maximum value, the respective block was replaced by a higher permeability block. The procedure was then repeated for a defined number of steps. This algorithm produced tree-like forms similar to the patterns observed in coffee sediment on a concave surface (Errera, M. R., Bejan, A., 1998, Deterministic Tree Networks for River Drainage Basin, Fractals, Vol. 6, No. 3, pp. 245-261).
Ordonez et al. (Ordonez, J. C., Bejan, A., Cherry, R. S., 2003, Designed Porous Media: Optimally Nonuniform Flow Structures Connecting One Point with More Points, International Journal of Thermal Science, Vol. 42, pp. 857-870) studied a similar porous media problem. Two criteria, highest pressure and highest-pressure gradient, were used to choose the replacement sequence among elements that share at least one face with the high permeability region. The comparison of these two criteria led to the conclusion that better results can be obtained using the pressure gradient option.
A more recent work by Boichot et al. presented an algorithm, called automaton by the authors, that searches for an optimized solution for the problem of how to effectively cool a heat generating surface by arranging the configuration of high conductivity material inside a fixed area (Boichot, R., Luo, L., Fan, Y., 2009, Tree-network Structure Generation for Heat Conduction by Cellular Automaton, Energy Conversion and Management, Vol. 50, pp. 376-386). This algorithm discretized the domain in simple elements and used the temperature gradient to determine the location where high conductivity material should be positioned. In Boichot et al. (Boichot, R., Luo, L., Fan, Y., 2009, Tree-network Structure Generation for Heat Conduction by Cellular Automaton, Energy Conversion and Management, Vol. 50, pp. 376-386), all the high conductivity material was initially placed inside the computational domain, and at each solution step, elements having high conductivity exchanged their position with elements having low conductivity. Additionally, elements having high conductivity are more expensive than elements having low conductivity, and as such, this approach is limiting.
The search for the minimization of the maximum temperature in similar problems has been reported by Ledezma et al. (Ledezma, G. A., Bejan, A., Errera, M. R., 1997, Constructal Tree Networks for Heat Transfer, Journal of Applied Physics, Vol. 82, No. 1, pp. 89-100), Boichot et al. (Boichot, R., Luo, L., Fan, Y., 2009, Tree-network Structure Generation for Heat Conduction by Cellular Automaton, Energy Conversion and Management, Vol. 50, pp. 376-386), and Almogbel and Bejan (Almogbel, M., Bejan, A., 1999, Conduction Trees with Spacings at the Tips, International Journal of Heat and Mass Transfer, Vol. 42, pp. 3739-3756), but an optimum solution has yet to be found.
Accordingly, what is needed is an improved, more effective cooling system and cooling system generator for PCBs. However, in view of the art considered as a whole at the time the present invention was made, it was not obvious to those of ordinary skill how the art could be advanced.
While certain aspects of conventional technologies have been discussed to facilitate disclosure of the invention, Applicants in no way disclaim these technical aspects, and it is contemplated that the claimed invention may encompass one or more of the conventional technical aspects discussed herein.
The present invention may address one or more of the problems and deficiencies of the prior art discussed above. However, it is contemplated that the invention may prove useful in addressing other problems and deficiencies in a number of technical areas. Therefore, the claimed invention should not necessarily be construed as limited to addressing any of the particular problems or deficiencies discussed herein.
In this specification, where a document, act or item of knowledge is referred to or discussed, this reference or discussion is not an admission that the document, act or item of knowledge or any combination thereof was at the priority date, publicly available, known to the public, part of common general knowledge, or otherwise constitutes prior art under the applicable statutory provisions; or is known to be relevant to an attempt to solve any problem with which this specification is concerned.